# Analytic Transport from Weak to Strong Coupling in the O(N) model

## TL;DR

This paper calculates an exact second-order transport coefficient in the large N limit of the 3+1d O(N) model across all couplings, providing insights into transport properties from weak to strong coupling regimes.

## Contribution

It provides the first exact non-perturbative calculation of the curvature-matter coupling in the O(N) model at large N for any coupling value.

## Key findings

- Exact expression for the transport coefficient $ppa$ at large N.
- Results are free from cut-off artifacts below the Landau pole.
- Predictions applicable to N=1 scalar field theory with  interaction.

## Abstract

In this work, a second-order transport coefficient (the curvature-matter coupling $\kappa$) is calculated exactly for the 3+1d O(N) model at large N for any coupling value. Since the theory is `trivial' in the sense of possessing a Landau pole, the result for $\kappa$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $\phi^4$ interaction.